Question

Please help I give 100 points​

Answer 1

Answer:

88, 102, 116

Step-by-step explanation:

$\bold{METHOD\ 1:}$

$a_1=18\\\\a_2=18+14=32\\\\a_3=32+14=46\\\\a_4=46+14=60\\\\a_5=60+14=74\\\\a_6=74+14=88\\\\a_7=88+14=102\\\\a_8=102+14=116$

$\bold{METHOD\ 2:}$

$a_1=18\\\\a_2=18+14=32\\\\a_3=32+14=46\\\\a_4=46+14=60\\\\a_5=60+14=74\\\vdots\\\\\text{It's an arithmetic sequence with first term}\ a_1=18\\\text{and the common difference}\ d=14.\\\\\text{The explicit formula of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{Substitute:}\\\\a_n=18+(n-1)(14)\qquad\text{use the distributive property}\\\\a_n=18+14n-14\\\\a_n=4+14n$

$\text{Substitute}\ n=6,\ 7\ \text{and 8}:\\\\a_6=4+14(6)=4+84=88\\\\a_7=4+14(7)=4+98=102\\\\a_8=4+14(8)=4+112=116$

Answer 2

Answer:

The next three numbers are 88, 102, 116

Step-by-step explanation:

Step 1:  Find the sequence

32 - 18 = 14

46 - 32 = 14

60 - 46 = 14

So... each number is added 14 to make the next number.

Step 2:  Find the rest of the number.

74 + 14 = 88

88 + 14 = 102

102 + 14 = 116

Answer:  The next three numbers are 88, 102, 116